I don´t know details about internal situation in Estonia. But based on experience from wolf hunting debates in Czechia and Slovakia, it is indeed farmers, farmer associations, local politicians from rural areas, hunters and hunter associations who demand introduced/increased wolf hunting quota. And they are supported also by a large part of "public". Depending what percentage of "public" agrees and how governmental politicians are inclined, hunting quota are set.
In Slovakia, each year this debate is done again and again. It is pretty heated, often with petitions signed by tens of thousand people for both sides, slashed tyres, demonstations.
In Czechia, farmers get mad about stock losses despite damage payments they receive. Many hunters dislike returning predators because they eat "their game stock". Some journalists add oil to the fire because it brings more readers. And some CZ people involved in politics, either in local, CZ or EU parliament, do support hunt quota because it can bring them obviously votes.
Survival of wolves in densely populated Central Europe is never-ending battle.